I have made this thread a CW thread. The answers here are extensive and very useful, but could still use enhancement and updates. I encourage the community to add to the answers below if they notice anything is missing. Please conform to the format of each existing post, and do not heavily modify the existing format of each one. Additions and corrections to the existing contents are encouraged.
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jrista♦Aug 6 '10 at 7:06

Leica Rangefinder and SLR Lenses

Leica RF and SLR lenses use the following terms to indicate features of each lens:

Common

XYZmm: Focal length

f/x.y: Maximum aperture

Lens Mount

xxx-R: Lens for the R (35mm SLR) system

xxx-M: Lens for the M (rangefinder) system

xxx-S: Lens for the S (MF DSLR) system

Lens Speed

Noctilux: Fastest lenses with max aperture around 1.0

Summilux: f/1.4 lens

Summicron: f/2 lens

Summarit: f/2.4 or f/2.5 lens

Elmarit: f/2.8 lens

Super Elmar, Elmar, Tele-Elmar: f/3.4+ lens

Telyt: f/3.4 telephoto lens

Vario-Elmar: Zoom version of Elmar (see above)

Features

ASPH: Lens with aspherical elements

APO: Lens with apochromatic correction

Note: There are sometimes small numbers engraved next to the infinity symbol on the focusing scale. These numbers indicate a difference of the actual focal length of the lens compared to the nominal value in tenths of millimeter. For example, if the number is 14 and the lens is 50mm, the actual focal length is 51.4.

Nikon F-Mount Lenses

Nikon SLR/DSLR lenses use the following terms to indicate features of each lens:

Common

XYZmm: Focal length

f/x.y: Maximum aperture (or f/a.b-c.d for variable aperture zooms)

Lens System

DX: Digital, Short Back, for 23.6mm x 15.6mm sensor.

FX: Full Frame (film or digital), for 36mm x 24mm sensor.

Lens Mount

AI: Automatic Indexing mount (includes metering sensor)

AI-S: Improved Automatic Indexing mount

IX: Lenses designed specially for APS film SLR-s; their rear end protrudes too much to allow using them on a 35mm film camera or a dSLR

Series E A cheaper series of AI-S where plastic replaced some metal parts. Not designated as Nikkor but "Nikon Lens Series E"

D: Distance, communicates focus distance for 3D Matrix metering mode and also for flash autoexposure. All AF-I, AF-S, and G-type lenses are also D-type. (Indicated after the f-number in the name, sometimes designated as AF-D).

Tamron Lenses

Tamron lenses use the following terms to indicate features of each lens. Tamron offers a considerable degree of functional features and lens types, particularly lens types that affect chromatic aberration:

@jrista: I can't edit your post, but here is what I would throw in: Some Nikon DSLRs, especially lower end ones (D40, D3000, D5000) do not have a built-in autofocus motor and require AF-S lenses for autofocus. I don't know about AF-I and AF-N though.
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Josh GoldshlagJul 16 '10 at 23:21

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@Lazer: If you mean "what is 1:1 magnification", it means that when you focus on a subject at the proper distance, it's image is projected onto the focal plane at "life size". That means if you take a macro shot of a bee, which is about 3/4 of an inch long, it will be 3/4 of an inch long on your camera sensor (or film.) You get a one-to-one magnification, its not blown up or shrunk, when imaged by your sensor or film.
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jrista♦Jul 17 '10 at 19:03

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@Lazer: That would generally be specific to each lens. A lot of the time, differences between a I and a II or a II and a III are subtle, but important. Other times they are significant. I recommend reading the-digital-picture.com/Reviews for details on lenses.
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jrista♦Jul 18 '10 at 9:57

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This is now Community Wiki, and as such, is editable by anyone. I have not been able to find rich detail for other common lens types, such as Lecia, Pentax, FourThirds, etc. I encourage those of you who have the knowledge to improve the content of this answer. Please, *conform to the existing format for any new lens entries. Please maintain the same level of quality and accuracy. If you don't have full information, post what information you do have under the proper section and lens heading.
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jrista♦Aug 6 '10 at 7:08

The top answer covers the decoding of the letters very well. I thought I might add a few comments as to what some of the features actually mean in terms of consequences of the features (it took me a while to work out what some of them meant).

Lenses only for reduced frame DSLRs

Most low to mid range DSLRs have a sensor that is smaller than a 35mm film frame - sometimes called "reduced frame" or "cropped sensor". So using a "full frame" lens will mean lots of extra light around the sensor that isn't used. You can makes lenses smaller and lighter by reducing the projected image size to fit the sensor size. However using these lenses on a full frame camera would result in the corners of the image being dark - and mostly these lenses won't fit on a full frame camera.

The "less than full frame" codes are:

Canon: EF-S (EF for full frame)

Nikon: DX (FX for full frame)

Pentax: DA (FA or D FA for full frame)

Sigma: DC (DG for full frame)

Sony/Minolta: DT

Tamron: Di II (Di for full frame)

Image Stabilisation/Vibration Reduction

Image Stabilisation is also called Optical Stabilisation, Optical Image Stabilisation, Optical Steady Shot, Vibration Compensation and Vibration Reduction. Does what it says on the tin basically. (Although note that some DSLR bodies have a form of vibration reduction in the body and so don't need it in the lens).

Canon: IS

Nikon: VR

Panasonic: OIS

Sigma: OS

Sony/Minolta: OSS

Tamron: VC

Fast and Quiet Focussing Motors

The focussing motors in some lower end lenses can be quite noisy. The higher end lenses are able to focus more quickly (the movements can be more accurately controlled) and are quieter and use less battery. The acronym for it usually includes "Sonic":

Canon: USM Ultrasonic Motor

Nikon: SWM Silent Wave Motor

Olympus/Zuiko: SWD Supersonic Wave Drive

Pentax: SDM Supersonic Drive Motor

Sigma: HSM Hyper-Sonic Motor

Sony/Minolta: SSM Super-Sonic Motor

Tamron: USD Ultrasonic Silent Drive

Lens Features

There are a variety of lens features to reduce chromatic abberations (where different colours don't exactly converge) and other imperfections in lens performance. In particular

aspherical lens elements have a more complex surface profile that can reduce or eliminate spherical aberration and also reduce other optical aberrations compared to a simple lens.

low dispersion glass means that there is a relatively small difference in the amount different colours bend while going through the glass (technically the refractive index does not vary so much with wavelength), which reduces chromatic aberration.

apochromatic lens elements are very good at reducing chromatic aberration - they are generally made up of three different materials stuck together.

Lens Coatings

There are a variety of lens coatings used to reduce internal reflections and other possible problems. Internal reflections can end up producing ghost images or adding to lens flare. Not all lens manufacturers specify the lens coatings they use.

Macro

Macro lenses can focus very close to the end of the lens, providing (at least) a 1:1 ratio between the size of the object and the size of the image on the sensor. In plain english, you can take very close up shots of flowers, insects and so on. They are just called Macro (or occasionally Micro), making life easy for once.

Focusing

This includes Internal/Inner Focusing (IF) and (Internal) Rear Focusing (RF or IRF). Both of these reduce the number of individual lenses moving inside the lens. They also mean that the front of the lens will not move in or out, or rotate, during focusing. The lack of rotation can be important if, say, you have a circular polarizing filter, or a graded ND filter fitted to the lens. And the front not moving in or out can be important if the lens is very close to the subject.

High End Lenses

Some manufacturers have a code to indicate their high end lenses:

Canon: L Luxury

Pentax: ★ and Limited

Sigma: EX Professional EXternal lens body finishing

Sony: G Gold Series

Tamron: SP Super Performance

Miscellaneous

Other codes might indicate the mount type (which will indicate whether it will fit your body), whether it will work with a Teleconverter or whether the lens needs the camera body to provide the motor for auto-focussing.

Note that I'm not an expert at this and am happy to integrate clarifications left in comments.

Great stuff! I've noticed that a lot of lens manufacturers explicitly list the lens element features they use. Canon does not explicitly list every detail about their lenses with their feature codes, however it should be noted that they do use special lens elements. Canon lenses do use the following: UD (ultralow dispersion) Glass, Aspherical Lenses, Flourite Lenses, Diffractive Optics. Canon lenses also use advanced milticoating on both the front and internal lens elements. Not really sure why they don't publicize that much, but, there it is.
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jrista♦Jul 29 '10 at 17:32

I like Canon's naming scheme the best as it is most readable, and easier to name it when discussing a lens. When looking at other lenses it is easy to miss a small detail in the long acronym list.
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Michael NielsenJan 11 '13 at 7:16

Hamish: maybe add an explanation to the IS/VR explanation how the lens does it by having a gyro and accelerometer and moving one of the elements to compensate?
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Michael NielsenJan 11 '13 at 7:21